Definition:Composition (Combinatorics)

Definition

A $k$-composition of a (strictly) positive integer $n \in \Z: n > 0$ is an ordered $k$-tuple:

$c = \left({c_1, c_2, \ldots, c_k}\right)$

such that:

• $c_1 + c_2 + \cdots + c_k = n$
• $\forall i \in \left[{1 \, . \, . \, k}\right]: c_i \in \Z, c_i > 0$, that is, all the $c_i$ are strictly positive integers.